But that note also says that my encrypted credit card number may also have been accessed. I have used my credit card in the past to purchase software from Adobe, but those were one-time transactions. I've not joined any subscription service, in particular creative cloud.

So here's my question. Why do you need to keep my credit card number in your database after the transaction has been completed?

Everyone else in this thread is missing the point.

Your credit card number may have been accessed. Everybody with an Adobe account got the exact same letter. Cloud users, non Cloud users, whatever. They may or may not actually have your card on file, they're not customizing this message specifically for your situation and account. I got the message for an account that has NO purchase history, and I got it for an account that is signed onto Cloud too.

What the message says is that they were compromisedand sensitive financial details were leaked. Yours may be among them. It may not. They are unable or unwilling to say the extent of the damage, so the easy approach is just to tell everyone the same exact warning to watch their accounts etc.

Yea, that's probably true. And disappointing. It would be a simple database check to say whether or not they have my credit card number on file. They're holding themselves to a pretty minimal standard of service to their customers, which seems consistent with many of their other actions in last few years.

Additionally note that transaction histories frequently include partial numbers (last 4 digits is very common) and that's often unencrypted plaintext. It's printed on practically every receipt you get with a credit card purchase, but there are situations in which that data can be exploited.